Download evolution and natural selection

NVC
Evolution Lab
Bio110
EVOLUTION AND NATURAL SELECTION
INTRODUCTION
When there is genetic variation in a population, some individuals are better fit (or suited) to their
environment. As a result, individuals with that trait will be more successful at competing for
resources, and survive to reproduce in higher numbers than other members of the population.
These genetic variants would then appear more frequently among subsequent generations. Such
changes in the frequency with which alleles (varying forms of genes) appear in populations is
called evolution. The mechanism driving these changes is natural selection (i.e. the environment
selects individuals that are best fit for the current environmental conditions).
GOALS AND OBJECTIVES
1.
2.
3.
4.
5.
Understand the mechanism of natural selection
Understand how natural selection leads to evolutionary change.
Know the importance of genetic variation and competition for resources.
Understand basic statistical parameters and how they’re used
Propose a hypothesis, asses data, and draw a conclusion
Evolution: Traits in a population vary among individuals; evolution is a change in the frequency
of traits. Biological evolution changes populations, not individuals.
Natural Selection: The differential success in survival and reproduction among members of a
population. It occurs through an interaction between the environment and genetic variability
inherent among individual organisms making up the population. The process results in
adaptations to the environment (increased fitness).
Adaptation: Some heritable aspect of form, function, or behavior that improves the odds for
surviving and reproducing. Adaptations are environment specific and an outcome of natural
selection
Genetic Equilibrium: Populations experiencing long periods without changes in allele
frequencies (i.e. not evolving)
Results of Natural Selection
Three possible outcomes:
Directional Selection
Allele frequencies shift in consistent direction over time
Stabilizing Selection
Intermediate forms are favored and extremes are eliminated.
Disruptive Selection
Happens when forms at both ends of the range of variation are favored
Intermediate forms are selected against
Page 1
NVC
Evolution Lab
Elementary Statistics
Notation and Symbols:
Bio110
x
1
N
 xi
•
∑ is sigma (Greek capital S)
– This means to add, or sum, all observations of variable “x”
•
i (index variable, or counter) The index variable is used to identify any observation (e.g.
test subject number 2, measurement number 8, etc).
•
N is the total number of observations
•
xi : is the value of observation number i (e.g. the actual height of test subject 2, the
actual temperature measured for observation 8).
•
x: the mean of observations as the sum of values divided by number of observations
•
 is the hypothetical mean for ALL populations. For example, we cannot measure the
height of every individual person on earth, but we know there’s a universal mean.
•
represents the theoretical standard deviation for ALL populations.
•
Null hypothesis
•
Alternate hypothesis
•
Normal Distribution: The hypothetical frequency of outcomes plotted against the range
of possible events. This bell-shaped frequency distribution is so prevalent in nature that
it is considered “normal”. The mathematical characterization of such a distribution forms
the foundation of some statistical analyses.
Page 2
NVC
Evolution Lab
Bio110
Mean: the average value of observations; determined by
adding up all values then dividing them by the number
of observations. This parameter is limited to describing
the mean of only our observed values.
x
 xi
1
N
Variance: is an estimate of the range of values:
s x2
xi  x 2


N 1
Standard deviation is another estimate of the range of values in relation to the mean.
The square root of the variance equals one standard deviation (distance) from the mean:
sx 
Page 3
 xi  x 2
N 1

 xi2  Nx 2
N 1
NVC
Evolution Lab
Confidence Interval: probability that a spread of
values will lie within a specific part of the distribution
range (100% of observations should fall inside the bell
shape). This also provides our level of confidence for
testing hypotheses. Note that 95% of data fall within
the non-shaded parts of the curve and ~2 standard
deviations, while the shaded “tails” contain the
remaining 5%.
Bio110


CI  X 1  X 2  t
s12
s2
 2
n1
n2
t-Distribution: Allows us to compare two populations using the relative distances between their
respective means.
Critical Value: This value is derived from a t-Distribution table (see page 9) and can be viewed
as the distance (in standard deviations) among the population means being compared.
t
x  y 


 N x  1s x2  N y  1 s 2y  N x  N y


N

N

2

 N x N y
x
y




df  N x  N y  2
t- Statistic value: This value is calculated using experimental data and compared to the Critical
Value. When the t-value is greater than the critical value, a significant difference exists between
two groups.
p-value: The probability of arriving at an incorrect conclusion based on the data being analyzed.
Page 4
NVC
Evolution Lab
Bio110
Applying Statistics and the Student t-Test
We can compare populations (or any data sets) by plotting their respective frequency
distributions as in the following examples. Notice how the plotted distributions in Example 1 are
so far apart that one could easily conclude that there’s a significant difference. One could not
easily conclude that there’s a difference among the groups in Example 2. Unfortunately, we
can’t base our conclusions on simply viewing the data. This is where statistical analyses become
a valuable tool.
6
25
5
20
N
TEMP
4
3
15
2
1
250200150100 50 0 50 100150200250
Count
Count
Example 1- A clear, significant difference
TAXON
Pelv
Porph
TREATMENT
10
60 50 40 30 20 10 0 10 20 30 40 50 60
Count
Count
Example 2- A subtle difference
There are a great many statistical analyses used to analyze data. Which methods are applied
depend on the nature of the data and the hypothesis we’re testing. Remember that in the
scientific method, hypotheses must be falsifiable. Statistical analyses provide a way to
mathematically determine whether we can reject (or fail to reject) hypotheses with a certain level
of confidence.
The Student t-Test is one method for comparing two groups or the “equality of two means”.
By convention, the Null Hypothesis () is that there’s no significant difference between the
means (=). The Alternate Hypothesis () is that a significant difference does exist (≠).
Please note that we can test our hypotheses no matter what we predict the outcome will be. If we
believe there is a significant difference among groups, we simply hope our data will allow us to
reject the Null Hypothesis. We’ll choose a level of confidence then calculate the probability (pvalue) that we’ll erroneously reject the Null Hypothesis.
The Student t-Test was developed by William S. Gosset (1876-1937), an employee of the Guinness Brewing Company in Ireland.
Because Guinness did not allow publication of its research, Gosset published under the pseudonym “Student”.
Page 5
None
Shade
NVC
Evolution Lab
Bio110
EXPERIMENT IN NATURAL SELECTION
One of the great pieces of research examining natural selection and evolution involves Darwin’s
finches on the Galapagos Islands. In a crude reproduction of the experiment, you will first play
the part of the birds foraging for seeds then become the scientists analyzing the data.
To conduct the experiment, we will propose a hypothesis and collect data to test it. We will then
use a statistical analysis to determine whether the data support the hypothesis.
Null Hypothesis (H0): We propose that genetic variation in beak size/shape has NO EFFECT on
foraging ability.
Alternate Hypothesis (H1): Variation in beak size has a SIGNIFICANT EFFECT on foraging
ability.
Experimental Procedure: We will use the number of “seeds consumed” as the parameter for
foraging efficiency among different beak types.
Tweezers vs Clothespins
1.
2.
3.
4.
5.
Work in groups of at least 4
Two people will be birds (one with tweezer-shaped beaks, one with clothespins)
A third person will keep track of time (a stop watch or timer set for 1 min.)
The fourth person will count the number of seeds ingested.
When the two “birds” are ready, they begin foraging by placing seeds into the small
finger bowl or “bird stomach” for 1 minute.
6. The “timer” signals the end of the minute and the “counter” records the number of seeds
in each “bird stomach”.
7. Repeat these trials, rotating roles until you’ve collected data for 10 (ten) observations.
Enter results into the table on the following page.
8. Calculate the mean (average) of seeds consumed for each beak type and subtract the two.
9. Determine “critical value” from the t-Distribution table on the last page of this hand-out.
a. We’re testing at a 95% confidence level, so use the p= 0.05 column (100%
expressed as a decimal: 1.0 -.95 = 0.05). This means we’re setting a 0.05 limit on
the probability of arriving at an incorrect conclusion.
b. Find the Degrees of Freedom for our experiment. (Df = total number of
observations minus the number of groups we’re comparing).
c. Find the “critical value” where the Df row and p= 0.05 column intersect.
10. Enter your raw data into the instructor’s Excel spreadsheet to check your calculations and
determine whether you observed significant differences in foraging efficiency among
beak types.
Page 6
NVC
Evolution Lab
Bio110
EXPERIMENT RESULTS:
Data Collected
Observation (Xi)
1
2
3
4
5
6
7
8
9
10
Mean
Variance (from instructor)
SD (from instructor)
Critical value (from table)
t-value (from instructor)
p-value (from instructor)
Beak type 1 (tweezers)
Beak type 2 (clothespin)
Results/Conclusion:
1. Is the t- value you obtained higher than the critical value?
2. Do your results support the Null Hypothesis that there’s NO significant difference in
beak foraging efficiency?
3. From the p-value you obtained, what is the probability that you might erroneously reject
the Null Hypothesis?
Page 7
NVC
Evolution Lab
Bio110
SUMMARY QUESTIONS:
1. Based on your data, what conclusions can you make about the effect of beak shape on
foraging efficiency?
2. What do you think caused the differences in beak shapes among these birds?
3. What might happen to these birds, over time, if their populations do not interbreed?
4. What evolutionary process would be observed here if only one type of beak survived after a
few generations? (Hint: the process involves differential reproductive success among individuals
of varying traits within a population.)
5. What outcome of environment specific natural selection would be exhibited by the surviving
birds?
6. Although natural selection affects an individual’s survival or reproductive success,
adaptations occur at what level?
7. The statistical parameter we use to measure the average value for a number of observations is
called the ________
8. What statistical parameter gives values at specific (standard) distances from the mean?
9. The bell-shaped frequency distribution is so prevalent in nature that it is referred to as a
______________ distribution
10. The amount of variation in a population is measured using what statistical parameter?
11. The t-test is a useful tool in studying differences among two populations. What null
hypothesis does it test?
Page 8
NVC
Evolution Lab
t-Distribution Table:
Confidence level:
Page 9
95%
97.5%
99%
99.5%
Bio110